Bounds for the Genus of Generalized Total Graph of a Commutative Ring

Asir, T.; Mano, K.

doi:10.1142/s1005386719000385

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Genus Of Generalized Total Graphs1

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2021

2022

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Cited by 3 publications

(1 citation statement)

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“…Recently, Asir and Mano [19] obtained several bounds on the genus for the graph T (Γ I (R)). As a consequence some of the results given in the previous section are generalized.…”

Section: Genus Of Generalized Total Graphsmentioning

confidence: 99%

Genus of total graphs from rings: A survey

Chelvam

Asir

2018

AKCE International Journal of Graphs and Combinatorics

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“…Recently, Asir and Mano [19] obtained several bounds on the genus for the graph T (Γ I (R)). As a consequence some of the results given in the previous section are generalized.…”

Section: Genus Of Generalized Total Graphsmentioning

confidence: 99%

Genus of total graphs from rings: A survey

Chelvam

Asir

2018

AKCE International Journal of Graphs and Combinatorics

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A Survey on Genus of Selected Graphs from Commutative Rings

Asir

Mano

Subathra³

2021

Springer Proceedings in Mathematics &Amp; Statistics

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On the Nonorientable Genus of the Generalized Unit and Unitary Cayley Graphs of a Commutative Ring

Khorsandi

Musawi

2022

Algebra Colloq.

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Let [Formula: see text] be a commutative ring and [Formula: see text] the multiplicative group of unit elements of [Formula: see text]. In 2012, Khashyarmanesh et al. defined the generalized unit and unitary Cayley graph, [Formula: see text], corresponding to a multiplicative subgroup [Formula: see text] of [Formula: see text] and a nonempty subset [Formula: see text] of [Formula: see text] with [Formula: see text], as the graph with vertex set [Formula: see text]and two distinct vertices [Formula: see text] and [Formula: see text] being adjacent if and only if there exists [Formula: see text] such that [Formula: see text]. In this paper, we characterize all Artinian rings [Formula: see text] for which [Formula: see text] is projective. This leads us to determine all Artinian rings whose unit graphs, unitary Cayley graphs and co-maximal graphs are projective. In addition, we prove that for an Artinian ring [Formula: see text] for which [Formula: see text] has finite nonorientable genus, [Formula: see text] must be a finite ring. Finally, it is proved that for a given positive integer [Formula: see text], the number of finite rings [Formula: see text] for which [Formula: see text] has nonorientable genus [Formula: see text] is finite.

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Bounds for the Genus of Generalized Total Graph of a Commutative Ring

Cited by 3 publications

References 16 publications

Genus of total graphs from rings: A survey

Genus of total graphs from rings: A survey

A Survey on Genus of Selected Graphs from Commutative Rings

On the Nonorientable Genus of the Generalized Unit and Unitary Cayley Graphs of a Commutative Ring

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